A new Conversations View where users can easily track all of their chats in a unified window. If you prefer the old view can disable this in the Chat options;
We have a brand new Call View;
Improved call audio quality
Improving video call quality and support for more cameras.

In addition, there are numerous minor improvements. These include:

Improved chat synchronization
new presence and emoticon icons
the ability to store and view phone numbers in a Skype contact's profile
much lower chance Skype for Linux will crash or freeze
chat history loading is now much faster
support for two new languages: Czech and Norwegian.

Microsoft also warns “the very first time you start Skype for Linux 4.0 might take a few minutes (depending on how lengthy your chat history is). In the event, as I've started to tinker with the new Skype, Skype on Linux Mint 13 on my Lenovo ThinkPad T520 took less than a 30-seconds.

Formally, the new Skype for Linux is available for the 32 and 64-bit versions of Ubuntu 10.04 and Debian 6.0 and the 32-bit versions of Fedora 16 and openSUSE 12.1 . From my own experience I can also say that it will work on later versions of Ubuntu and related Linux distributions. The overall requirements are minimal: Qt 4.6.0, D-Bus 1.0.0, libasound2 1.0.18 with both PulseAudio 1.0 and BlueZ 4.0.0 being optional. Without a source code option, though, you're much stuck with the Debian/Ubuntu, Red Hat, and SUSE Linux families.